The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x+\sin y=\sin (x+y)$ and $|x|+|y|=1$ is

If $5 \sin h x-\cos h x=5$, then one of the values of $\tan h x$ is

The smallest positive value (in degrees) of $\theta$ for which $\tan \left(\theta+100^{\circ}\right)=\tan \left(\theta+50^{\circ}\right) \tan (\theta) \tan \left(\theta-50^{\circ}\right)$ is valid, is